Lanthanide-Dependent Clustering in Yb$^{3+}$/Ln$^{3+}$ Co-Doped CaF$_2$ Nanocrystals: Correlating Spectroscopic Signatures with DFT Insights

The formation of heterogeneous lanthanide-ion clusters in CaF$_2$ was investigated experimentally and computationally. CaF$2$ nanoparticles co-doped with 20mol% Yb$^{3+}$ and 2mol% Ln$^{3+}$ (Ln$^{3+}$ = Ce$^{3+}$, Pr$^{3+}$, Nd$^{3+}$, Sm$^{3+}$, Eu$^{3+}$, Gd$^{3+}$, Ho$^{3+}$, Er$^{3+}$, and Tm$^{3+}$) were synthesized via a hydrothermal method. The structural and morphological properties were characterized using powder X-ray diffraction, dynamic light scattering, and transmission electron microscopy techniques. High-resolution Fourier transform infra-red spectroscopy revealed the presence of Yb$^{3+}$ isolated cubic centers and various cluster sites. The relative concentration of the clusters varied with the choice of the co-doping ion. Calculations based on density functional theory were used to estimate the formation energies and local coordination structures of different clusters. The calculations indicate that the neutral $C{4v}$ aggregations containing Ln$^{3+}$ tend to decrease across the lanthanide series, while the negatively charged derivatives of hexameric clusters are relatively constant. This variation matches the experimental results. This study advances understanding of the clustering mechanisms in lanthanide-doped CaF$_2$ nanoparticles and has implications for luminescence optimization in advanced nanomaterials.

💡 Research Summary

This work investigates the formation of heterogeneous lanthanide‑ion clusters in calcium fluoride (CaF₂) nanocrystals that are co‑doped with a high concentration of ytterbium (20 mol % Yb³⁺) and a low concentration of a second trivalent lanthanide (2 mol % Ln³⁺, where Ln = Ce, Pr, Nd, Sm, Eu, Gd, Ho, Er, Tm). The authors synthesize the nanoparticles by a hydrothermal route (190 °C, 6 h) using sodium citrate as a capping agent, and they confirm that all samples retain the cubic fluorite structure (space group Fm 3̅ m) through powder X‑ray diffraction. Scherrer analysis of the (111) diffraction peak yields crystallite sizes of 10–12 nm, while dynamic light scattering and transmission electron microscopy give hydrodynamic diameters of 13–19 nm, indicating well‑dispersed, roughly spherical particles.

High‑resolution Fourier‑transform infrared (FTIR) spectroscopy performed at 10 K reveals the characteristic Yb³⁺ ²F₇/₂ → ²F₅/₂ transition (≈10 325–10 400 cm⁻¹) together with two lower‑energy absorption features that the authors label “cluster peak 1” (≈10 225 cm⁻¹) and “cluster peak 2” (≈10 265 cm⁻¹). The spectra are normalized to the isolated cubic Yb³⁺ site to allow comparison across samples. While the intensity of cluster 2 remains essentially constant for all co‑dopants, the intensity (area) of cluster 1 varies dramatically, being strongest for Ce³⁺ and Pr³⁺ co‑doping and weakest for Tm³⁺. Gaussian deconvolution shows that cluster 1 is broader, suggesting it comprises several overlapping geometries, whereas cluster 2 is sharper.

To rationalize these observations, the authors perform density‑functional‑theory (DFT) calculations using VASP with PAW‑PBE potentials. A 3 × 3 × 3 supercell (≈162 atoms) of CaF₂ is constructed, and a series of defect clusters are modeled: (i) isolated Yb³⁺ on a Ca site (Oₕ symmetry), (ii) C₃ᵥ and C₄ᵥ neutral clusters where a Yb³⁺ and an Ln³⁺ share a Ca site and are charge‑compensated by a fluorine interstitial (Fᵢ⁻), (iii) three‑ion clusters (³Ln·Ca:3Fᵢ) and (iv) six‑ion hexameric clusters (⁶Ln·Ca:8V·13Fᵢ) that carry a net negative charge. Formation energies are computed with full charge‑correction schemes (image‑charge and potential‑alignment terms) and expressed as functions of the chemical potentials of Ca²⁺, F⁻, Yb³⁺ and Ln³⁺, constrained by the stability condition μ_Ca²⁺ + 2μ_F⁻ = μ_CaF₂.

The calculated formation energies reveal two systematic trends across the lanthanide series. First, the neutral C₄ᵥ clusters become progressively more stable from the early lanthanides (Ce³⁺) to the later ones (Tm³⁺), with a drop of roughly 0.3 eV in formation energy. This reflects the decreasing ionic radius and the resulting better lattice accommodation of the smaller Ln³⁺ ions. Second, the negatively charged hexameric clusters have formation energies that are essentially invariant (within ±0.05 eV) throughout the series, indicating that their stability is governed primarily by the overall charge‑balance rather than the specific lanthanide size.

Using Boltzmann statistics (c_i ≈ g_i exp